ASPEN, Colo. -- Shortly after New Jersey Gov. Chris Christie took to the stage with three fellow Republican governors here Thursday, he derided self-serving politicians who try to be all things to all people and are afraid to alienate anyone.

By the end of the session, hosted by the nonpartisan Aspen Institute, Christie put his potential 2016 presidential hopes where his mouth is. And in the process, he set himself apart from -- and risked alienating --- a very significant and growing swath of the Republican Party led by Sen. Rand Paul: libertarians.

After relatively tame remarks by his fellow Republicans about the increasing libertarian strain in the GOP, Christie unleashed an unprompted and full-throated broadside against the trending movement and its supporters, who in the House this week nearly helped passed an amendment that would reduce funding for the National Security Agency phone records collection program.

“As a former prosecutor who was appointed by President George W. Bush on Sept. 10, 2001, I just want us to be really cautious,” Christie said, “because this strain of libertarianism that’s going through both parties right now and making big headlines, I think, is a very dangerous thought.”

Christie was then asked whether his remarks pertained to Paul (R-Ky.), a leading libertarian-minded conservative who is also thought to be a leading 2016 presidential contender.

He didn’t back down, suggesting Paul and his ilk had “amnesia” about Sept. 11.

“You can name any one of them that’s engaged in this,” Christie said. “I want them to come to New Jersey and sit across from the widows and the orphans and have that conversation. … I’m very nervous about the direction this is moving in.”

Christie’s colleagues on the stage, given the chance to weigh in on his remarks, stayed far away from them.

The vote on reducing NSA funding failed in the House by a 217-205 vote, with 94 of the chamber’s 234 Republicans voting in favor – a very significant level of support for something that a few years ago likely wouldn’t have been close to passing.

Republicans, writ large, have generally played nice with the libertarian element of the party, recognizing its growing influence since concerns about privacy and the Obama Administration’s surveillance programs have grown.

Going back to the 2012 presidential campaign, in fact, Republicans have recognized that libertarians – once the marginalized supporters of Paul’s father, presidential candidate Ron Paul – are a growing force in the GOP.

Paul's supporters said Christie is disregarding a very important -- and very American -- right to privacy.

“Defending America and fighting terrorism is the concern of all Americans, especially Sen. Paul,” Paul’s former chief of staff, Doug Stafford, said. “But it can and must be done in keeping with our constitution and while protecting the freedoms that make America exceptional.”

And Paul himself tweeted a response early Friday morning:

Christie worries about the dangers of freedom. I worry about the danger of losing that freedom. Spying without warrants is unconstitutional.

Taken another way, Christie’s remarks could be seen as laying down a marker in a potential matchup with Paul – pitting the party’s still-dominant hawkish foreign policy wing against the new brand of libertarians.

Those close to Christie chalked up his remarks to his genuine and personal beliefs rather than any political gamesmanship – particularly given the hundreds of New Jerseyans who died on Sept. 11.

GOP strategists said it’s part of a healthy dialogue that should continue through the 2016 campaign, whether or not Christie and Paul both run.

“We don't all have to agree on everything to be good Republicans,” said GOP strategist Henry Barbour. “These sorts of candid policy discussions are healthy for the party and the country. Gov. Christie is not afraid to share his views on tough issues, and that's one of the reasons he has such broad support in New Jersey.”

Added Scott Reed, who managed Bob Dole’s 1996 presidential campaign: “Once again, Christie is the canary in the coal mine on the fork in the road for the GOP on a major aspect of foreign policy. In 2015, the GOP debate will shift to developing a winning message for 2016, and Christie should be in the front row of the choir.”

Polling shows Republicans are conflicted about the government’s surveillance programs.

According to a Washington Post-ABC News poll this week, more than six in 10 Republicans say it’s more important for the government to investigate terrorism threats, even if it intrudes on personal privacy, while about one-third choose personal privacy as their priority.

But 77 percent of Republicans said the NSA’s surveillance of phone records intrudes on Americans’ privacy rights. (They were split evenly on whether it intrudes on their own personal privacy rights.)

Indiana Gov. Mike Pence (R), who spoke alongside Christie at the forum and served on the House Judiciary Committee that passed legislation in response to the Sept. 11 attacks, agreed that the debate is good for the party.

“I think it is healthy and welcome, always,” he said. “Because when you’re dealing with issues of national security … there always is that careful balancing between taking those actions necessary to protect the American people from harm and carefully weighing that against a vigorous American commitment to personal liberty and to privacy.”

Another participant, Louisiana Gov. Bobby Jindal, said libertarians are “absolutely” ascending in the GOP and said it’s a result of the Obama White House.

“I think you’re seeing more and more (political) expressions – and I think that’s a good thing,” Jindal said. “I think in part this libertarian revival you’re seeing is a response to our president, who believes in a bigger government.”

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